Astrophysics (Index)About

minimum mass

(m sin i)
(measured bound on the mass of an exoplanet)

A minimum mass (often labeled m sin i) can sometimes be determined for an extra-solar planet or other companion (e.g., brown dwarf or binary-star companion) even if the actual mass cannot, and often it is a minimum mass that is reported. A quantity labeled m sin i represents the mass of the planet times the sine of the orbital inclination from the user's perspective (called i, with 0° meaning the orbit is observed "from above", i.e., in a plane perpendicular to the line of sight, and 90° meaning mean viewed edge-on). This minimum mass matches the actual mass (m) if the inclination is 90° (when sin i = 1). Otherwise, sin i is less than one and this minimal mass is less than the companion's actual mass (m).

It is expressed in this manner because the orbital inclination is generally not revealed by observation, constituting a missing factor in calculating the companion's mass. This is the case if the star's mass has been determined (e.g., stellar mass determination), and the RV method has revealed the companion. RV observations yield the radial velocity and the orbital period. Knowing the orbital speed as well would be enough information to complete the derivation of the mass, and also knowing the orbital inclination would reveal the speed. The orbital speed is always, at minimum, the magnitude of the measured relative radial velocity of the host and companion.

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